Re: Adding two numbers of high precision results in a number of low precision??

To: mathgroup at smc.vnet.net

Subject: [mg56981] Re: Adding two numbers of high precision results in a number of low precision??

From: "Peltio" <peltio at trilight.zone>

Date: Thu, 12 May 2005 02:32:14 -0400 (EDT)

References: <d5mv2v$dv0$1@smc.vnet.net>

Reply-to: "Peltio" <peltioNOSPAM at despammed.com.invalid>

Sender: owner-wri-mathgroup at wolfram.com

"Kees van Schaik" wrote
>> Precisie bTemp[3,0,0] = 389.685
>> Precisie Q[3,1] = 390.729
>> Precisie bTemp[3,0,1] =53.8232
>
>
>Now the first one makes sense, but the last one, how is it possible that
>if I add two numbers of precision ca. 390 I get something of precision
>53 back?
Cancellation of significant digits?
*If* the two numbers have different signs, this could happen.
For example:
a=+2.1234567895
b=-2.1234567891
a+b=0.4*10^-10
The first two numbers have a precision of 11 digits. Their sum has a
precision of 1.
cheers,
Peltio
PS
To see this in Mathematica, you should experiment with numbers with more then 16
digits, lest not to fall in the machine precision Maelstrom.
a = +2.3333333333333333335;
b = -2.333333333333331245;
Precision[a]
Precision[b]
Precision[a + b]